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math.NT2009★ 1 cited
Rank statistics for a family of elliptic curves over a function field
Carl Pomerance, Igor E. Shparlinski
We show that the average and typical ranks in a certain parametric family of elliptic curves described by D. Ulmer tend to infinity as the parameter . This is perhaps…
math.NT2007
On Pseudosquares and Pseudopowers
Carl Pomerance, Igor E. Shparlinski
Introduced by Kraitchik and Lehmer, an -pseudosquare is a positive integer that is a quadratic residue for each odd prime , yet is not a square. We use…
math.NT2005
Sieving by large integers and covering systems of congruences
Michael Filaseta, Kevin Ford, Sergei Konyagin +2
An old question of Erdos asks if there exists, for each number N, a finite set S of integers greater than N and residue classes r(n) mod n for n in S whose union is all the integer…